# Non uniform Quantization in PCM

Quantization has been divided into two types

1. Uniform Quantization.
2. Non-Uniform Quantization.
 Uniform Quantization Non-Uniform Quantization $\Delta$$\Delta$ is constant through out Quantization process. $\Delta$$\Delta$is variable that is the step size is variable. characteristics of the Quantizer are linear. ex:- Mid-tread type Quantizer. Mid-rise type Quantizer. characteristics of the Quantizer are  Non-linear.

we know that the sampled version of message signal is Quantized. The Quantization process may follow a Quantization law , which is uniform in general.

But in tele – communication applications like PCM telephony however it is preferable to use a variable separation between the representation levels.

i.e, Non-Uniform Quantization law is to be followed.

for example the range of voltages covered by voice signals from the peaks of loud talk to the weak passages of weak talk is on the order of 1000 to 1.

weak passages (weak talk) which need more protection can be Quantized with smaller step size.

and loud talk will be Quantized with large step size.

Need for Non-Uniform Quantization for speech signal (or) Need for companding in PCM:-

as said above weak talk can be protected more than that of loud talk of a speech signal.

Since at the receiving end of a telephone system a loud talk can be received with tolerable reduced voltage but a weak talk can not be received if the voltage level is reduced during Quantization process.

we know that speech and music signals are characterized by large crest factor.

for a signal with large crest factor, the signal to noise ratio is given by

$SQR=\frac{P}{N_{q}}=\frac{Signal&space;Power}{Noise&space;Power}$ .

if we keep  $\Delta$ as constant that is Uniform Quantization is applied then noise power  $N_{q}&space;=&space;\frac{\Delta&space;^{2}}{12}$  is almost constant.

$SQR\propto&space;P$ .

SQR is proportional to signal power .

if signal power is low  then SQR also becomes low which is inevitable at the receiver.

if signal power is high then SQR also becomes high which is desirable at the receiver.

to maintain constant SQR at the receiving end companding is preferred in a PCM system (or) for the transmission of voice / speech / Music signals.

i.e, for low power levels of input signal  $\Delta$ is reduced

$\therefore&space;N_{q}&space;=\frac{\Delta&space;^{2}}{12}$ becomes less and $\because&space;\frac{S}{N_{q}}&space;=\frac{P}{N_{q}}$ is improved.

similarly for high power level $\Delta$  is increased ,

P is more Noise power increases and SQR is reduced.

In this way , SQR is maintained uniform throughout the Quantization process.

This Uniform Quantization can be achieved through companding.

companding in PCM :-

1. is required to improve SQR of weak signals.
2. is also known as Non-Uniform Quantization.

In practical it is difficult to implement the Non-Uniform Quantization because it is not known in advance hoe the signal level is varying?

we follow a particular method as mentioned below

1. Before the application of the signal to a Uniform Quantizer in the Transmitter weak signals are being amplified and strong signals are being attenuated.
2. then uniform Quantization is used on the modified signal.
3. At the receiver a reverse process is to be done.

in general compander is a combination of two devices a compressor(at the Transmitter) and an expander (at the receiver).

the use of Non-Uniform Quantizer is equivalent to passing the base band signal through a compressor passing through a compressor and then applying the compressed signal to a uniform Quantizer.

a particular compression law is used in practice the so called -law and A-law .

to restore the signal samples to their correct relative values we must use a device in the receiver with a characteristic  complementary  to the compressor such a device is called as an expander.

ideally, the compression and expansion laws are exactly inverse.

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